A spokeswoman tells Fox News, "The governor's focus remains on the final five days of the session. We still have a lot of important work to get done for the people of Texas. The governor has had no intention of running."

But a longtime Perry adviser tells Fox, "As he has said, all this attention would cause any human to think about his options...the media in Texas is laser-focused on this issue, and in any tea leaf as news."

Perry is the longest-serving governor in Texas history and won an unprecedented third four-year term last November.